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a smooth horizantal table is rotating at an angular speed W about its vertical axis .a groove is made on the surface along a radius .a partical is gently placed inside the groove at a distance of a from the center .the speed of the particle with respect to the table at a distance of x from its center

a smooth horizantal table is rotating at an angular speed W about its vertical axis .a groove is made on the surface along a radius  .a partical is gently placed inside the groove at a distance of a from the center .the speed of the particle with respect to the table at a distance of x from its center

Grade:12th pass

1 Answers

Priyanshu Gujjar
101 Points
2 months ago

Let v be the velocity of the particle w.r.t the table at the instant the particle is at a distance  x.

When the particle is at a distance  a from the centre, at that instant its velocity is zero.
Using          ar=dxvdv                         where  ar=xw2
    xw2=dxvdv
OR         0Vvdv=w2aLxdx
 
OR         2v20V=w2×2x2aL                 
 
OR       V20=w2(L2a2)         V=wL2a2

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